Motivations: Such distributed problems on specialization have been considered in [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}. References [2]}, [3]}, [4]}, [5]}, [7]} are oriented towards distributed offline problems. In [6]}, the authors proposed an online algorithm by adopting a local dynamic programming relaxation strategy, while Lee et al. [1]} designed two distributed online dual averaging algorithms with the help of the idea of [15]} and the broadcast-based subgradient push [16]}, respectively. Regrettably, the privacy concerns are ignored in the existing works on specialization. Compared to the well-studied differential privacy on overlap, how to do differential privacy on specialization remains largely unexplored. It is of interest, therefore, to apply privacy mechanisms to the distributed problems on specialization.
